Evolution Strategies for Deep Neural Network Models Design
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AI, Robots, and Swarms: Issues, Questions, and Recommended Studies
AI, Robots, and Swarms Issues, Questions, and Recommended Studies Andrew Ilachinski January 2017 Approved for Public Release; Distribution Unlimited. This document contains the best opinion of CNA at the time of issue. It does not necessarily represent the opinion of the sponsor. Distribution Approved for Public Release; Distribution Unlimited. Specific authority: N00014-11-D-0323. Copies of this document can be obtained through the Defense Technical Information Center at www.dtic.mil or contact CNA Document Control and Distribution Section at 703-824-2123. Photography Credits: http://www.darpa.mil/DDM_Gallery/Small_Gremlins_Web.jpg; http://4810-presscdn-0-38.pagely.netdna-cdn.com/wp-content/uploads/2015/01/ Robotics.jpg; http://i.kinja-img.com/gawker-edia/image/upload/18kxb5jw3e01ujpg.jpg Approved by: January 2017 Dr. David A. Broyles Special Activities and Innovation Operations Evaluation Group Copyright © 2017 CNA Abstract The military is on the cusp of a major technological revolution, in which warfare is conducted by unmanned and increasingly autonomous weapon systems. However, unlike the last “sea change,” during the Cold War, when advanced technologies were developed primarily by the Department of Defense (DoD), the key technology enablers today are being developed mostly in the commercial world. This study looks at the state-of-the-art of AI, machine-learning, and robot technologies, and their potential future military implications for autonomous (and semi-autonomous) weapon systems. While no one can predict how AI will evolve or predict its impact on the development of military autonomous systems, it is possible to anticipate many of the conceptual, technical, and operational challenges that DoD will face as it increasingly turns to AI-based technologies. -
A Covariance Matrix Self-Adaptation Evolution Strategy for Optimization Under Linear Constraints Patrick Spettel, Hans-Georg Beyer, and Michael Hellwig
IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. XX, NO. X, MONTH XXXX 1 A Covariance Matrix Self-Adaptation Evolution Strategy for Optimization under Linear Constraints Patrick Spettel, Hans-Georg Beyer, and Michael Hellwig Abstract—This paper addresses the development of a co- functions cannot be expressed in terms of (exact) mathematical variance matrix self-adaptation evolution strategy (CMSA-ES) expressions. Moreover, if that information is incomplete or if for solving optimization problems with linear constraints. The that information is hidden in a black-box, EAs are a good proposed algorithm is referred to as Linear Constraint CMSA- ES (lcCMSA-ES). It uses a specially built mutation operator choice as well. Such methods are commonly referred to as together with repair by projection to satisfy the constraints. The direct search, derivative-free, or zeroth-order methods [15], lcCMSA-ES evolves itself on a linear manifold defined by the [16], [17], [18]. In fact, the unconstrained case has been constraints. The objective function is only evaluated at feasible studied well. In addition, there is a wealth of proposals in the search points (interior point method). This is a property often field of Evolutionary Computation dealing with constraints in required in application domains such as simulation optimization and finite element methods. The algorithm is tested on a variety real-parameter optimization, see e.g. [19]. This field is mainly of different test problems revealing considerable results. dominated by Particle Swarm Optimization (PSO) algorithms and Differential Evolution (DE) [20], [21], [22]. For the case Index Terms—Constrained Optimization, Covariance Matrix Self-Adaptation Evolution Strategy, Black-Box Optimization of constrained discrete optimization, it has been shown that Benchmarking, Interior Point Optimization Method turning constrained optimization problems into multi-objective optimization problems can achieve better performance than I. -
Natural Evolution Strategies
Natural Evolution Strategies Daan Wierstra, Tom Schaul, Jan Peters and Juergen Schmidhuber Abstract— This paper presents Natural Evolution Strategies be crucial to find the right domain-specific trade-off on issues (NES), a novel algorithm for performing real-valued ‘black such as convergence speed, expected quality of the solutions box’ function optimization: optimizing an unknown objective found and the algorithm’s sensitivity to local suboptima on function where algorithm-selected function measurements con- stitute the only information accessible to the method. Natu- the fitness landscape. ral Evolution Strategies search the fitness landscape using a A variety of algorithms has been developed within this multivariate normal distribution with a self-adapting mutation framework, including methods such as Simulated Anneal- matrix to generate correlated mutations in promising regions. ing [5], Simultaneous Perturbation Stochastic Optimiza- NES shares this property with Covariance Matrix Adaption tion [6], simple Hill Climbing, Particle Swarm Optimiza- (CMA), an Evolution Strategy (ES) which has been shown to perform well on a variety of high-precision optimization tion [7] and the class of Evolutionary Algorithms, of which tasks. The Natural Evolution Strategies algorithm, however, is Evolution Strategies (ES) [8], [9], [10] and in particular its simpler, less ad-hoc and more principled. Self-adaptation of the Covariance Matrix Adaption (CMA) instantiation [11] are of mutation matrix is derived using a Monte Carlo estimate of the great interest to us. natural gradient towards better expected fitness. By following Evolution Strategies, so named because of their inspira- the natural gradient instead of the ‘vanilla’ gradient, we can ensure efficient update steps while preventing early convergence tion from natural Darwinian evolution, generally produce due to overly greedy updates, resulting in reduced sensitivity consecutive generations of samples. -
A Restart CMA Evolution Strategy with Increasing Population Size
1769 A Restart CMA Evolution Strategy With Increasing Population Size Anne Auger Nikolaus Hansen CoLab Computational Laboratory, CSE Lab, ETH Zurich, Switzerland ETH Zurich, Switzerland [email protected] [email protected] Abstract- In this paper we introduce a restart-CMA- 2 The restart CMA-ES evolution strategy, where the population size is increased for each restart (IPOP). By increasing the population The (,uw, )-CMA-ES In this paper we use the (,uw, )- size the search characteristic becomes more global af- CMA-ES thoroughly described in [3]. We sum up the gen- ter each restart. The IPOP-CMA-ES is evaluated on the eral principle of the algorithm in the following and refer to test suit of 25 functions designed for the special session [3] for the details. on real-parameter optimization of CEC 2005. Its perfor- For generation g + 1, offspring are sampled indepen- mance is compared to a local restart strategy with con- dently according to a multi-variate normal distribution stant small population size. On unimodal functions the ) fork=1,... performance is similar. On multi-modal functions the -(9+1) A-()(K ( (9))2C(g)) local restart strategy significantly outperforms IPOP in where denotes a normally distributed random 4 test cases whereas IPOP performs significantly better N(mr, C) in 29 out of 60 tested cases. vector with mean m' and covariance matrix C. The , best offspring are recombined into the new mean value (Y)(0+1) = Z wix(-+w), where the positive weights 1 Introduction w E JR sum to one. The equations for updating the re- The Covariance Matrix Adaptation Evolution Strategy maining parameters of the normal distribution are given in (CMA-ES) [5, 7, 4] is an evolution strategy that adapts [3]: Eqs. -
Neuroevolution Strategies for Episodic Reinforcement Learning ∗ Verena Heidrich-Meisner , Christian Igel
J. Algorithms 64 (2009) 152–168 Contents lists available at ScienceDirect Journal of Algorithms Cognition, Informatics and Logic www.elsevier.com/locate/jalgor Neuroevolution strategies for episodic reinforcement learning ∗ Verena Heidrich-Meisner , Christian Igel Institut für Neuroinformatik, Ruhr-Universität Bochum, 44780 Bochum, Germany article info abstract Article history: Because of their convincing performance, there is a growing interest in using evolutionary Received 30 April 2009 algorithms for reinforcement learning. We propose learning of neural network policies Available online 8 May 2009 by the covariance matrix adaptation evolution strategy (CMA-ES), a randomized variable- metric search algorithm for continuous optimization. We argue that this approach, Keywords: which we refer to as CMA Neuroevolution Strategy (CMA-NeuroES), is ideally suited for Reinforcement learning Evolution strategy reinforcement learning, in particular because it is based on ranking policies (and therefore Covariance matrix adaptation robust against noise), efficiently detects correlations between parameters, and infers a Partially observable Markov decision process search direction from scalar reinforcement signals. We evaluate the CMA-NeuroES on Direct policy search five different (Markovian and non-Markovian) variants of the common pole balancing problem. The results are compared to those described in a recent study covering several RL algorithms, and the CMA-NeuroES shows the overall best performance. © 2009 Elsevier Inc. All rights reserved. 1. Introduction Neuroevolution denotes the application of evolutionary algorithms to the design and learning of neural networks [54,11]. Accordingly, the term Neuroevolution Strategies (NeuroESs) refers to evolution strategies applied to neural networks. Evolution strategies are a major branch of evolutionary algorithms [35,40,8,2,7]. -
Evolutionary Computation Evolution Strategies
Evolutionary computation Lecture Evolutionary Strategies CIS 412 Artificial Intelligence Umass, Dartmouth Evolution strategies Evolution strategies • Another approach to simulating natural • In 1963 two students of the Technical University of Berlin, Ingo Rechenberg and Hans-Paul Schwefel, evolution was proposed in Germany in the were working on the search for the optimal shapes of early 1960s. Unlike genetic algorithms, bodies in a flow. They decided to try random changes in this approach − called an evolution the parameters defining the shape following the example of natural mutation. As a result, the evolution strategy strategy − was designed to solve was born. technical optimization problems. • Evolution strategies were developed as an alternative to the engineer’s intuition. • Unlike GAs, evolution strategies use only a mutation operator. Basic evolution strategy Basic evolution strategy • In its simplest form, termed as a (1+1)- evolution • Step 2 - Randomly select an initial value for each strategy, one parent generates one offspring per parameter from the respective feasible range. The set of generation by applying normally distributed mutation. these parameters will constitute the initial population of The (1+1)-evolution strategy can be implemented as parent parameters: follows: • Step 1 - Choose the number of parameters N to represent the problem, and then determine a feasible range for each parameter: • Step 3 - Calculate the solution associated with the parent Define a standard deviation for each parameter and the parameters: function to be optimized. 1 Basic evolution strategy Basic evolution strategy • Step 4 - Create a new (offspring) parameter by adding a • Step 6 - Compare the solution associated with the normally distributed random variable a with mean zero offspring parameters with the one associated with the and pre-selected deviation δ to each parent parameter: parent parameters. -
A Note on Evolutionary Algorithms and Its Applications
Bhargava, S. (2013). A Note on Evolutionary Algorithms and Its Applications. Adults Learning Mathematics: An International Journal, 8(1), 31-45 A Note on Evolutionary Algorithms and Its Applications Shifali Bhargava Dept. of Mathematics, B.S.A. College, Mathura (U.P)- India. <[email protected]> Abstract This paper introduces evolutionary algorithms with its applications in multi-objective optimization. Here elitist and non-elitist multiobjective evolutionary algorithms are discussed with their advantages and disadvantages. We also discuss constrained multiobjective evolutionary algorithms and their applications in various areas. Key words: evolutionary algorithms, multi-objective optimization, pareto-optimality, elitist. Introduction The term evolutionary algorithm (EA) stands for a class of stochastic optimization methods that simulate the process of natural evolution. The origins of EAs can be traced back to the late 1950s, and since the 1970’s several evolutionary methodologies have been proposed, mainly genetic algorithms, evolutionary programming, and evolution strategies. All of these approaches operate on a set of candidate solutions. Using strong simplifications, this set is subsequently modified by the two basic principles of evolution: selection and variation. Selection represents the competition for resources among living beings. Some are better than others and more likely to survive and to reproduce their genetic information. In evolutionary algorithms, natural selection is simulated by a stochastic selection process. Each solution is given a chance to reproduce a certain number of times, dependent on their quality. Thereby, quality is assessed by evaluating the individuals and assigning them scalar fitness values. The other principle, variation, imitates natural capability of creating “new” living beings by means of recombination and mutation. -
Integrating Heuristiclab with Compilers and Interpreters for Non-Functional Code Optimization
Integrating HeuristicLab with Compilers and Interpreters for Non-Functional Code Optimization Daniel Dorfmeister Oliver Krauss Software Competence Center Hagenberg Johannes Kepler University Linz Hagenberg, Austria Linz, Austria [email protected] University of Applied Sciences Upper Austria Hagenberg, Austria [email protected] ABSTRACT 1 INTRODUCTION Modern compilers and interpreters provide code optimizations dur- Genetic Compiler Optimization Environment (GCE) [5, 6] integrates ing compile and run time, simplifying the development process for genetic improvement (GI) [9, 10] with execution environments, i.e., the developer and resulting in optimized software. These optimiza- the Truffle interpreter [23] and Graal compiler [13]. Truffle is a tions are often based on formal proof, or alternatively stochastic language prototyping and interpreter framework that interprets optimizations have recovery paths as backup. The Genetic Compiler abstract syntax trees (ASTs). Truffle already provides implementa- Optimization Environment (GCE) uses a novel approach, which tions of multiple programming languages such as Python, Ruby, utilizes genetic improvement to optimize the run-time performance JavaScript and C. Truffle languages are compiled, optimized and of code with stochastic machine learning techniques. executed via the Graal compiler directly in the JVM. Thus, GCE In this paper, we propose an architecture to integrate GCE, which provides an option to generate, modify and evaluate code directly directly integrates with low-level interpreters and compilers, with at the interpreter and compiler level and enables research in that HeuristicLab, a high-level optimization framework that features a area. wide range of heuristic and evolutionary algorithms, and a graph- HeuristicLab [20–22] is an optimization framework that provides ical user interface to control and monitor the machine learning a multitude of meta-heuristic algorithms, research problems from process. -
Evolution Strategies
Evolution Strategies Nikolaus Hansen, Dirk V. Arnold and Anne Auger February 11, 2015 1 Contents 1 Overview 3 2 Main Principles 4 2.1 (µ/ρ +; λ) Notation for Selection and Recombination.......................5 2.2 Two Algorithm Templates......................................6 2.3 Recombination Operators......................................7 2.4 Mutation Operators.........................................8 3 Parameter Control 9 3.1 The 1/5th Success Rule....................................... 11 3.2 Self-Adaptation........................................... 11 3.3 Derandomized Self-Adaptation................................... 12 3.4 Non-Local Derandomized Step-Size Control (CSA)........................ 12 3.5 Addressing Dependencies Between Variables............................ 14 3.6 Covariance Matrix Adaptation (CMA)............................... 14 3.7 Natural Evolution Strategies.................................... 15 3.8 Further Aspects............................................ 18 4 Theory 19 4.1 Lower Runtime Bounds....................................... 20 4.2 Progress Rates............................................ 21 4.2.1 (1+1)-ES on Sphere Functions............................... 22 4.2.2 (µ/µ, λ)-ES on Sphere Functions.............................. 22 4.2.3 (µ/µ, λ)-ES on Noisy Sphere Functions........................... 24 4.2.4 Cumulative Step-Size Adaptation.............................. 24 4.2.5 Parabolic Ridge Functions.................................. 25 4.2.6 Cigar Functions....................................... -
Simplify Your Cma-Es 3
ACCEPTED FOR: IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 Simplify Your Covariance Matrix Adaptation Evolution Strategy Hans-Georg Beyer and Bernhard Sendhoff Senior Member, IEEE Abstract—The standard Covariance Matrix Adaptation Evo- call the algorithm’s peculiarities, such as the covariance matrix lution Strategy (CMA-ES) comprises two evolution paths, one adaptation, the evolution path and the cumulative step-size for the learning of the mutation strength and one for the rank- adaptation (CSA) into question. Notably in [4] a first attempt 1 update of the covariance matrix. In this paper it is shown that one can approximately transform this algorithm in such has been made to replace the CSA mutation strength control a manner that one of the evolution paths and the covariance by the classical mutative self-adaptation. While getting rid of matrix itself disappear. That is, the covariance update and the any kind of evolution path statistics and thus yielding a much covariance matrix square root operations are no longer needed simpler strategy1, the resulting rank-µ update strategy, the so- in this novel so-called Matrix Adaptation (MA) ES. The MA- called Covariance Matrix Self-Adaptation CMSA (CMSA-ES) ES performs nearly as well as the original CMA-ES. This is shown by empirical investigations considering the evolution does not fully reach the performance of the original CMA- dynamics and the empirical expected runtime on a set of standard ES in the case of small population sizes. Furthermore, some test functions. Furthermore, it is shown that the MA-ES can of the reported performance advantages in [4] were due to a be used as search engine in a Bi-Population (BiPop) ES. -
Algorithm and Experiment Design with Heuristiclab Instructor Biographies
19.06.2011 Algorithm and Experiment Design with HeuristicLab An Open Source Optimization Environment for Research and Education S. Wagner, G. Kronberger Heuristic and Evolutionary Algorithms Laboratory (HEAL) School of Informatics, Communications and Media, Campus Hagenberg Upper Austria University of Applied Sciences Instructor Biographies • Stefan Wagner – MSc in computer science (2004) Johannes Kepler University Linz, Austria – PhD in technical sciences (2009) Johannes Kepler University Linz, Austria – Associate professor (2005 – 2009) Upper Austria University of Applied Sciences – Full professor for complex software systems (since 2009) Upper Austria University of Applied Sciences – Co‐founder of the HEAL research group – Project manager and chief architect of HeuristicLab – http://heal.heuristiclab.com/team/wagner • Gabriel Kronberger – MSc in computer science (2005) Johannes Kepler University Linz, Austria – PhD in technical sciences (2010) Johannes Kepler University Linz, Austria – Research assistant (since 2005) Upper Austria University of Applied Sciences – Member of the HEAL research group – Architect of HeuristicLab – http://heal.heuristiclab.com/team/kronberger ICCGI 2011 http://dev.heuristiclab.com 2 1 19.06.2011 Agenda • Objectives of the Tutorial • Introduction • Where to get HeuristicLab? • Plugin Infrastructure • Graphical User Interface • Available Algorithms & Problems • Demonstration • Some Additional Features • Planned Features • Team • Suggested Readings • Bibliography • Questions & Answers ICCGI 2011 http://dev.heuristiclab.com -
Metaheuristics for Multiobjective Optimization
Metaheuristics for Multiobjective Optimization Carlos A. Coello Coello CINVESTAV-IPN Depto. de Computaci´on Av. Instituto Polit´ecnicoNacional No. 2508 Col. San Pedro Zacatenco M´exico,D. F. 07300, MEXICO [email protected] 1 Motivation Most problems in nature have several (possibly conflicting) objectives to be satisfied. Many of these problems are frequently treated as single-objective optimization problems by transforming all but one objective into constraints. 2 A Formal Definition The general Multiobjective Optimization Problem (MOP) can be formally defined as: ∗ ∗ ∗ ∗ T Find the vector ~x = [x1, x2, . , xn] which will satisfy the m inequality constraints: gi(~x) ≤ 0 i = 1, 2, . , m (1) the p equality constraints hi(~x) = 0 i = 1, 2, . , p (2) and will optimize the vector function ~ T f(~x) = [f1(~x), f2(~x), . , fk(~x)] (3) 3 What is the notion of optimum in multiobjective optimization? Having several objective functions, the notion of “optimum” changes, because in MOPs, we are really trying to find good compromises (or “trade-offs”) rather than a single solution as in global optimization. The notion of “optimum” that is most commonly adopted is that originally proposed by Francis Ysidro Edgeworth in 1881. 4 What is the notion of optimum in multiobjective optimization? This notion was later generalized by Vilfredo Pareto (in 1896). Although some authors call Edgeworth-Pareto optimum to this notion, we will use the most commonly accepted term: Pareto optimum. 5 Definition of Pareto Optimality We say that a vector of decision variables ~x∗ ∈ F is Pareto optimal ∗ if there does not exist another ~x ∈ F such that fi(~x) ≤ fi(~x ) for ∗ all i = 1, .